Representations of Wave Functions

At this point it is important to remember that wave functions give the probability of where the electron is. A three dimensional wave function is a three dimensional shape (like a sphere for example) the size of this shape and the surface it encloses is tells use the probability density which we can use to predict the probability of an electron being in a given position at a particular time. The wave function is NOT the path the electron travels, NOR is it the shape of the electron.

In chemistry the word orbital is used to represent the "location" of an electron in an atom. An orbital is a surface in which there is a 90% probability of finding the electron inside. The orbital is an extremely useful tool for getting the general "shape" of an atom. All orbitals with one value of l (angular quantum number) have the same shape.

We will now use a computer program developed at Boston University to have a look at orbitals. It is possible to run the program online but BU has an incredibly slow server and you will probably go mad waiting for it to load. The solution is to download the program onto your computer's hard drive. Go to the web page below, click on the link "easy install" follow the directions (it is best to save the program to your desk top so you can find it) and then have a cup of tea while you are waiting.

http://qsad.bu.edu/Applets/quantumexplorer/index.html

Open the program Atomic Explorer. This program allows you to look at the shape and probability density of the hydrogen orbitals.

Instructions

• On the left hand of the screen click on one of the hydrogen orbitals (e.g. try 1s first). A fuzzy green circle should appear on the left hand of the screen. This is green circle is a slice through the middle of the 1s orbital.
• In the lower right hand corner of the screen is a set of axis showing the position of the slice. There is a slider bar on the vertical scale, use this to look at slices in different positions.
• You can also change the two dimensional plane you are looking at XY, YZ or ZX.

Work your way through the orbitals of hydrogen having a look at the shapes they have. The green and purple shading shows the two possible phases of the matter wave in this orbital. The important things for you to get a feel for is the density of the color (be it green or purple), this shows the probability density for the electron in each orbital.

What do the black regions of the orbital plot represent?


No two electrons in an atom can have identical quantum numbers. This rule is called the Pauli Exclusion Principle and basically means that you cannot be in the same place with the same energy at the same time. For any two electrons in an atom they must have some difference in their wave function. This characteristic helps us define the number of electrons in each energy state.

You may already know from Chemistry that the 1s energy state usually can hold two electrons. Now this may seem to contradict the n, l and m quantum numbers we have defined so far. We have to introduce a forth and final parameter for classifying the electron called spin.

Electron spin is an intrinsic property of electrons, it was first identified when physicists studied the behavior of electrons in magnetic fields (e.g. the Zeeman Effect). An electron has two possible spin energy states which are called "up" and "down". Electron spin is more closely associated with energy that with something actually spinning.